Question

List the fractions from least to greatest. 2 3/6, 4 1/3, 1 3/4, 1 4/5

Answer 1

To compare the mixed numbers, let's first convert them to improper fractions:

1. \(2 \frac{3}{6} = \frac{2 \times 6 + 3}{6} = \frac{12 + 3}{6} = \frac{15}{6} = \frac{5}{2}\)

2. \(4 \frac{1}{3} = \frac{4 \times 3 + 1}{3} = \frac{12 + 1}{3} = \frac{13}{3}\)

3. \(1 \frac{3}{4} = \frac{1 \times 4 + 3}{4} = \frac{4 + 3}{4} = \frac{7}{4}\)

4. \(1 \frac{4}{5} = \frac{1 \times 5 + 4}{5} = \frac{5 + 4}{5} = \frac{9}{5}\)

Now, to compare these fractions, we can either find a common denominator or convert them to decimal form.

Converting to decimals:

1. \( \frac{5}{2} = 2.5\)
2. \( \frac{13}{3} \approx 4.33\) (which is \(4.333...\))
3. \( \frac{7}{4} = 1.75\)
4. \( \frac{9}{5} = 1.8\)

Now, arrange in order from least to greatest:

1. \(1 \frac{3}{4} (1.75)\)
2. \(1 \frac{4}{5} (1.8)\)
3. \(2 \frac{3}{6} (2.5)\)
4. \(4 \frac{1}{3} (4.33)\)

Thus, the order from least to greatest is:
1. \(1 \frac{3}{4}\)
2. \(1 \frac{4}{5}\)
3. \(2 \frac{3}{6}\)
4. \(4 \frac{1}{3}\)